When I want to write something longer than a tweet about something other than math or sci-fi, here is where I'll write it.

## Wednesday, August 26, 2009

### Wednesday Math, Vol. 85: Carl Friedrich Gauss, Genius And Jerk

In the book Men of Mathematics, author E.T. Bell begins the chapter on Carl Friedrich Gauss with this sentence. "Archimedes, Newton and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit."

That's an interesting list. Bell first published in 1937, and now, more than seven decades later, the general consensus on the great mathematicians, puts at least four people that category, including my close personal mathematical bud Leonhard Euler, and there are those who would also add names from the era after Gauss like David Hilbert, Henri Poincaré, John Von Neumann and Andrey Kolmogorov.

Where did the original list of three come from?

Well, hypothetical question asker, it came from... Carl Friedrich Gauss, indirectly.

Gauss said the three greatest mathematicians were Archimedes, Newton and Eisenstein. No, not Einstein, Eisenstein. (Einstein wasn't born until a generation after Gauss' death.) Eisenstein was one of Gauss' pupils late in the great man's life, and Eisenstein's first work is on elliptic curves, an important field to this day. But Eisenstein died young, so most mathematicians today wouldn't put him in the top three, and probably not even in the top ten. The list got changed over time, Eisenstein's name erased and his better known mentor's name put in his place.

It sounds modest of Gauss to give so much credit to Eisenstein, but I think he really wanted to put his own name on the list, but was slightly embarrassed to do so. Gauss belongs there, no doubt, but I subscribe to him these ulterior motives because Gauss was a dick.

I mean, not at Superman levels of dickishness, but for a real person, there are a lot of stories from his life that show very dickish tendencies.

Here's one from his early life. In early 1801, a Sicilian astronomer named Giuseppe Piazzi saw a dwarf planet through his telescope, about half the radius of Pluto but in a much closer orbit, and tracked the object's movement for about forty days. He named the rock after Ceres, the Roman goddess who was the favored protectress of Sicily back in the day. But after forty days, Piazzi lost track of Ceres and couldn't get it back in sight.

Into the story comes 24 year old Gauss. With a remarkable insight, he realizes that the few sightings made by Piazzi could be used to predict where Ceres should be, but the method to make good on the prediction would take solving a system of seventeen equations in seventeen variables. And so, he does it, and he sends his results off to some German astronomers, who re-locate Ceres in late 1801, and Gauss is an international celebrity.

When people ask how he made his prediction, he wouldn't tell them. Some accused him of sorcery. Clearly, this was a more superstitious time. Someone should have accused him of dickery.

Okay, that's young Gauss. How about old Gauss? Well, hypothetical, he's still a genius and still a jerk.

You might dimly remember from geometry class that Euclid starts his work with five postulates. The fifth postulate, known as the parallel hypothesis, could not be proven as a theorem, though many people tried throughout history. Its statement, that there is exactly one parallel line to a given line that passes through a given point not on the line, is so intuitive that the great German philosopher Immanuel Kant makes a proclamation that it must be true, largely because Kant is so super smart and he is willing to hold his breath until his face turns blue if anyone disagrees with him. Other mathematicians slightly better than Kant work at creating a geometry where the fifth postulate isn't true, including Farkas Bolyai, a student of Gauss', who passes on his obsession to his son, János. It's János who makes the progress that finds a consistent system, meaning no internal contradictions, where the parallel postulate does not hold, the first breakthrough step in creating the field now known as non Euclidean geometry. Farkas is so proud of his son that he sends the younger man's work to his old professor Gauss. Gauss writes back that he already knew everything János wrote and that it was kind of obvious.

The jerk.

There are two catches here. Non Euclidean geometry may have been kind of obvious to Gauss, but Gauss is a freaking genius. Even I don't deny this. I am here to proclaim his jerkitude, but I'm not idiot enough to say it cancels out his massive smart guy-ness. The second catch is that Gauss may have known this, but he never published it. He had made the decision that he didn't want to get into a pissing match with the ghost of Immanuel Kant, who was still a big damn deal in the world of German intellectual thought.

Let me conclude by saying that any list of great mathematicians that leaves off Gauss is clearly incomplete. But as I hear more stories from the great man's life, I become more and more convinced that I will never have a man crush on Gauss the way I love Lenny Euler.

That's just the way I roll.

~

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## 12 comments:

Fascinating post--Thank you. My own theory is that geniuses are always jerks. Our amazement when they're mean/self-serving/greedy-for-fame is irrational, sort of like being shocked that the stars in the heavens aren't nice to us or each other. I would love (and be amazed by) a Matty Boy post about a genius who is NOT a jerk!

A lot of the stories about Euler show a personal generosity, which is the source of my man crush on the guy.

Our own Matty Boy is a genius but not a jerk!

I told him that one day after I spent an afternoon with a genius who WAS a jerk, and he shot back with:

Matty Boy: Smarter than most nice people; Nicer than most smart people!

That's mah brudder!

Matty's just too damned nice to be a jerk, math genius be damned!

I gotta admit, though--I love brilliant but cocky bastards who can't tell you enough how smart they are, especially when they really ARE that smart. It's a weakness in me, I guess. But then, my heroes are Foghorn Leghorn and Bugs Bunny.

You do the math.

I did a post about Johnny Von Neumann a year ago, and it wasn't so much that he'd always tell you how smart he was as much as show you how smart he was. There are a mess of stories about him that are variations on this one.

A top mathematician at Cambridge is completely stuck on a problem. He calls up Von Neumann, asks for his help and explains the problem. Von Neumann steps off the train in Cambridge, hands the guy the complete solution he figured out in the hour of free time he had on the trip and catches the next train back to London.

The connecting theme of many of these stories is that someone needs his help and he's happy to do it. It's the personal generosity that sets him apart from people like Gauss or Newton, who played their cards very close to their chests.

"...someone needs his help and he's happy to do it." Yes, like the Cambridge mathematician Hardy recognizing Ramanujan's genius when this poor, ill, obscure Indian scholar sent him a letter packed with incredible theorems out of the blue...and helping him.

Gauss was not a "jerk" in the way it may appear today. He was instead so obssessed by perfection that he preferred to withhold publication of what he considered not to be "ripe" (complete and not subjected to criticism). And this was precisely the most important of his qualities: he introduced a new pattern of mathematical rigours which may have founded modern mathematics. In addition to that, he had a very "german", rigid education and suffered from many personal tragedies. In my humble opinion, Gauss was THE greatest mathematician of all times. Eric Bell invented the triunvirate only to avoid much controversy at the time.

Hi, Fabio. Eric Bell didn't invent the triumvirate as I wrote in the post. Also, any list of mathematicians prior to 1900 that doesn't include Euler is clearly incomplete.

As for personal tragedies, Euler went blind and kept working, and most of the stories I know about Euler show a great generosity of spirit, which only shows rarely with Gauss.

Gauss also said that if Euler's identity "was not immediately apparent to a student on being told it, the student would never be a first-class mathematician."

'Cause all first-class mathematicians are born with the background information needed to understand that formula already engraved in their brains, of course. Just further confirmation of dickishness.

This quote was from

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (New York: Penguin, 2004). Derbyshire, J.Some of the references are incorrect. Regarging to Non Euclidian Geometry, Gauss wrote that "to praise it would mean to praise myself", because he "had the same convictions for 54 years", which was proved to be right only after his death, when his "nachlass" (personal notebook) was encountered. However, in a letter to Gerling, he wrote "I consider the young geometer J. Bolyai a genius of the first rank".

Gauss also supported, encouraged and suggested Riemann to wrote his seminal thesis "On the foudations of geometry". Gauss' comment on the thesis was that it showed "... a gloriously fertile originality".

The above examples demonstrate that Gauss was not that jerk. Euler was a genius, but Gauss was God as a mathematician. In many important mathematicians' opinion, he was even superior to Newton and Archimedes. Euler could beasily be at the fourth place, which is still amazingly brilliant considering the competitors.

Gauss was very reserved as a person and this should not be confused with arrogance or "dickery". Here is a testimony of someone who knew him very well, his friend and mathematician Wolfgang Bolyai:

... and I became acquainted with Gauss, who was then a student there [Gottingen] and with whom I am still in friendly contact, though I could never compare myself with him. He was very modest and showed little; not for three days, as with Plato, but for years one could be with him without recognizing his greatness. (...) often we walked with one another, each of us occupied with hos own thoughts, for hours not exchanging a word".

Euler was indeed one of the greatest mathematicians ever, however Gauss basically reinvented the whole of mathematical world. I would dare to say that he was even greater than Newton and Archimedes: his work has more breadth and depth than anyone else's in recorded history.

I heard of Gauss solving a 17th degree binomial in the construction of the 17-gon, but not of him solving a 17th degree polynomial in 17 variables in the determination of Ceres' orbit. You're not confusing these situations, are you?

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